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Multiple Solutions for a Quasilinear Schrödinger Equation on \(\mathbb{R}^{N}\)

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Abstract

The multiplicity of positive weak solutions is established for quasilinear Schrödinger equations −L p u+(λA(x)+1)|u|p−2 u=h(u) in \(\mathbb{R}^{N}\), where L p u=ϵ p Δ p u+ϵ p Δ p (u 2)u, A is a nonnegative continuous function and nonlinear term h has a subcritical growth. We achieved our results by using minimax methods and Lusternik-Schnirelman theory of critical points.

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Acknowledgements

The authors thank the referee for his/her useful suggestions and comments.

Research of C.O. Alves partially supported by INCT-MAT, PROCAD and CNPq/Brazil 303080/2009-4.

Research of G.M. Figueiredo partially supported by supported by CNPq/Brazil 300705/2008-5.

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Authors and Affiliations

  1. Unidade Acadêmica de Matemática e Estatística, Universidade Federal de Campina Grande, 58429-900, Campina Grande, PB, Brazil

    Claudianor O. Alves

  2. Faculdade de Matemática, Universidade Federal do Pará, 66075-110, Belém, PA, Brazil

    Giovany M. Figueiredo

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  1. Claudianor O. Alves
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  2. Giovany M. Figueiredo
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Correspondence to Giovany M. Figueiredo.

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Alves, C.O., Figueiredo, G.M. Multiple Solutions for a Quasilinear Schrödinger Equation on \(\mathbb{R}^{N}\) . Acta Appl Math 136, 91–117 (2015). https://doi.org/10.1007/s10440-014-9942-8

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  • DOI: https://doi.org/10.1007/s10440-014-9942-8

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